The implementation of non-orthogonal multiple access (NOMA) and transmit antenna selection (TAS) technique has considered in this paper since TASaware base station (BS) provides the low cost, low complexity, and high diversity gains. In this paper, we investigate performance of two users by deriving outage probability. The system performance benefits from design of TAS and full-duplex (FD) scheme applied at NOMA users, and bandwidth efficiency will be enhanced although self-interference exists due to FD. The main contribution lies in the exact expressions of outage probability which are derived to exhibit system performance. Different from the simulated parameters, the analytical results show that increasing number of transmit antennas at the BS is way to improve system performance.